The Key Manager can be used by mod authors to prevent their mods from loading up on specific servers or for specific users.

Unfortunately, there are quite a few server owners that do not know about copyright or choose to ignore it. There even have been cases of bad people selling mods they do not own. The Key Manager is a way to make this copyright infringement more difficult.

No. Just because a mod uses the Key Manager now, this doesn't mean that you have to pay for it now. I strongly discourage charging for mods, but unfortunately, this doesn't mean that some mod authors won't use the Key Manager to charge for their mods now.

Your Valheim game or server will automatically request a new key for all mods from the Key Manager server periodically in the background. These keys are valid for a few days. If the Key Manager server is unavailable for some time, your gameplay is not affected.

For singleplayer games, Key Manager stores your SteamID and Steam username on its servers, if you are using Steam or your Xbox user ID and your Xbox username, if you are using Xbox.
For multiplayer games, Key Manager stores the IP address of your server and assigns a unique hash to your server on the first connection, to be able to react to IP address changes on your server and avoid interruption of your gameplay.
This information can be seen by the authors of the Key Manager mods you are using and the Key Manager admin and will be used for the purpose of Key Manager only.
All information will be deleted a few days after you've stopped using mods that use Key Manager.